Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long double a, b;
  cin >> a >> b;
  long double area = .5 * b;
  long double gh = area / a;
  vector<long double> vec;
  for (int i = 1; i < a; i++) {
    long double matlob = gh * i;
    long double s = 0, f = b, m, ans = -1, num;
    long long c = 0;
    while (c < 300) {
      m = (s + f) / 2;
      c++;
      num = (m * (m / b)) / 2;
      if (num - matlob <= 1e-9) {
        s = m;
        ans = m;
      } else if (num > matlob) {
        f = m;
      } else
        s = m;
    }
    vec.push_back(ans);
  }
  for (int i = 0; i < vec.size(); i++)
    cout << fixed << setprecision(15) << vec[i] << " ";
  return 0;
}